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On the Existence of Asymptotic-lp Structures in Banach Spaces

Published online by Cambridge University Press:  20 November 2018

Adi Tcaciuc
Adi Tcaciuc*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1 e-mail: tcaciuc@math.ualberta.ca
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Abstract

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It is shown that if a Banach space is saturated with infinite dimensional subspaces in which all “special” $n$-tuples of vectors are equivalent with constants independent of $n$-tuples and of $n$, then the space contains asymptotic-${{l}_{p}}$ subspaces for some $1\,\le \,p\,\le \,\infty $. This extends a result by Figiel, Frankiewicz, Komorowski and Ryll-Nardzewski.

Keywords

46B2046B4046B03
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 4 , 01 December 2007 , pp. 619 - 631
Copyright
Copyright © Canadian Mathematical Society 2007

References

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